scholarly journals Nonlinear multiscale simulation of instabilities due to growth of an elastic film on a microstructured substrate

2020 ◽  
Vol 90 (11) ◽  
pp. 2397-2412
Author(s):  
Iman Valizadeh ◽  
Oliver Weeger
Keyword(s):  
Deformation Gradient ◽  
Multiscale Simulation ◽  
Numerical Results ◽  
Unit Cell ◽  
Homogeneous Material ◽  
Two Phase ◽  
Biological Phenomena ◽  
Elastic Film ◽  
Living Tissues ◽  
Analytical Approaches

Abstract The objective of this contribution is the numerical investigation of growth-induced instabilities of an elastic film on a microstructured soft substrate. A nonlinear multiscale simulation framework is developed based on the FE2 method, and numerical results are compared against simplified analytical approaches, which are also derived. Living tissues like brain, skin, and airways are often bilayered structures, consisting of a growing film on a substrate. Their modeling is of particular interest in understanding biological phenomena such as brain development and dysfunction. While in similar studies the substrate is assumed as a homogeneous material, this contribution considers the heterogeneity of the substrate and studies the effect of microstructure on the instabilities of a growing film. The computational approach is based on the mechanical modeling of finite deformation growth using a multiplicative decomposition of the deformation gradient into elastic and growth parts. Within the nonlinear, concurrent multiscale finite element framework, on the macroscale a nonlinear eigenvalue analysis is utilized to capture the occurrence of instabilities and corresponding folding patterns. The microstructure of the substrate is considered within the large deformation regime, and various unit cell topologies and parameters are studied to investigate the influence of the microstructure of the substrate on the macroscopic instabilities. Furthermore, an analytical approach is developed based on Airy’s stress function and Hashin–Shtrikman bounds. The wavelengths and critical growth factors from the analytical solution are compared with numerical results. In addition, the folding patterns are examined for two-phase microstructures and the influence of the parameters of the unit cell on the folding pattern is studied.

Numerical Analysis of Two-Phase Pipe Flow of Liquid Helium Using Multi-Fluid Model

2001 ◽  
Vol 123 (4) ◽  
pp. 811-818 ◽  
Author(s):  
Jun Ishimoto ◽  
Mamoru Oike ◽  
Kenjiro Kamijo
Keyword(s):  
Phase Transition ◽  
Gas Phase ◽  
Liquid Helium ◽  
Two Phase Flow ◽  
Fluid Model ◽  
Numerical Results ◽  
Phase Flow ◽  
Two Dimensional ◽  
Two Phase ◽  
Normal Fluid

The two-dimensional characteristics of the vapor-liquid two-phase flow of liquid helium in a pipe are numerically investigated to realize the further development and high performance of new cryogenic engineering applications. First, the governing equations of the two-phase flow of liquid helium based on the unsteady thermal nonequilibrium multi-fluid model are presented and several flow characteristics are numerically calculated, taking into account the effect of superfluidity. Based on the numerical results, the two-dimensional structure of the two-phase flow of liquid helium is shown in detail, and it is also found that the phase transition of the normal fluid to the superfluid and the generation of superfluid counterflow against normal fluid flow are conspicuous in the large gas phase volume fraction region where the liquid to gas phase change actively occurs. Furthermore, it is clarified that the mechanism of the He I to He II phase transition caused by the temperature decrease is due to the deprivation of latent heat for vaporization from the liquid phase. According to these theoretical results, the fundamental characteristics of the cryogenic two-phase flow are predicted. The numerical results obtained should contribute to the realization of advanced cryogenic industrial applications.

Numerical and Experimental Investigation of Interface Bonding Via Substrate Remelting of an Impinging Molten Metal Droplet

1996 ◽  
Vol 118 (1) ◽  
pp. 164-172 ◽  
Author(s):  
C. H. Amon ◽  
K. S. Schmaltz ◽  
R. Merz ◽  
F. B. Prinz
Keyword(s):  
Heat Transfer ◽  
Numerical Model ◽  
Molten Metal ◽  
Thermal Stresses ◽  
Initial Conditions ◽  
Metal Droplet ◽  
Solid Substrate ◽  
Numerical Results ◽  
Operating Conditions ◽  
Analytical Approaches

A molten metal droplet landing and bonding to a solid substrate is investigated with combined analytical, numerical, and experimental techniques. This research supports a novel, thermal spray shape deposition process, referred to as microcasting, capable of rapidly manufacturing near netshape, steel objects. Metallurgical bonding between the impacting droplet and the previous deposition layer improves the strength and material property continuity between the layers, producing high-quality metal objects. A thorough understanding of the interface heat transfer process is needed to optimize the microcast object properties by minimizing the impacting droplet temperature necessary for superficial substrate remelting, while controlling substrate and deposit material cooling rates, remelt depths, and residual thermal stresses. A mixed Lagrangian–Eulerian numerical model is developed to calculate substrate remelting and temperature histories for investigating the required deposition temperatures and the effect of operating conditions on remelting. Experimental and analytical approaches are used to determine initial conditions for the numerical simulations, to verify the numerical accuracy, and to identify the resultant microstructures. Numerical results indicate that droplet to substrate conduction is the dominant heat transfer mode during remelting and solidification. Furthermore, a highly time-dependent heat transfer coefficient at the droplet/substrate interface necessitates a combined numerical model of the droplet and substrate for accurate predictions of the substrate remelting. The remelting depth and cooling rate numerical results are also verified by optical metallography, and compare well with both the analytical solution for the initial deposition period and the temperature measurements during droplet solidification.

Measurement of Liquid Film Thickness for Annular Two-Phase HFC134a Gas-Liquid Ethanol Flow in the Vertical Tube

2021 ◽  
Author(s):  
Huacheng Zhang ◽  
Tutomo Hisano ◽  
Shoji Mori ◽  
Hiroyuki Yoshida
Keyword(s):  
Film Thickness ◽  
Liquid Film ◽  
Thin Liquid Film ◽  
Atmospheric Condition ◽  
Heating Surface ◽  
Operating Conditions ◽  
Liquid Film Thickness ◽  
Two Phase ◽  
Disturbance Waves ◽  
Analytical Approaches

Abstract Annular gas-liquid two-phase flows, such as the flows attached to the fuel rods of boiling water reactors (BWR), are a prevalent occurrence in industrial processes. At the gas-liquid interface of such flows, disturbance waves with diverse velocity and amplitude commonly arise. Since the thin liquid film between two successive disturbance waves leads to the dryout on the heating surface and limits the performance of the BWRs, complete knowledge of the disturbance waves is of great importance for the characterized properties of disturbance waves. The properties of disturbance waves have been studied by numerous researchers through extensive experimental and analytical approaches. However, most of the experimental data and analyses available in the literature are limited to the near atmospheric condition. In consideration of the properties of liquids and gases under atmospheric pressure which are distinct from those under BWR operating conditions (7 MPa, 285 °C), we employed the HFC134a gas and liquid ethanol whose properties at relatively low pressure and temperature (0.7 MPa, 40 °C) are similar to those of steam and water under BWR operating conditions as working fluids in a tubular test section having an inside diameter 5.0mm. Meanwhile, the liquid film thickness is measured by conductance probes. In this study, we report the liquid film thickness characteristics in a two-phase HFC134a gas-liquid ethanol flow. A simple model of the height of a disturbance wave was also proposed.

Coefficients of thermal expansion of unidirectional fiber-reinforced composites using unit-cell model

2018 ◽  
Vol 53 (11) ◽  
pp. 1425-1436
Author(s):  
PC Upadhyay ◽  
JP Dwivedi ◽  
VP Singh
Keyword(s):  
Thermal Expansion ◽  
Cell Model ◽  
Unit Cell ◽  
Fiber Reinforced Composites ◽  
Reinforced Composites ◽  
Unit Cell Model ◽  
Fiber Reinforced ◽  
Two Phase ◽  
Thermal Expansion Coefficients ◽  
Three Phase

Coefficients of thermal expansion of some uniaxially fiber-reinforced composites have been evaluated using three-phase unit-cell model. Results have been compared with the values predicted by two other models based on composite cylinders assembly (CCA), and also with some earlier reported experimental values. An extension of the two-phase unit-cell model has also been presented for the evaluation of thermal expansion coefficients of three-phase composites. The formulation has been used to evaluate the overall coefficients of thermal expansion of AS-graphite/epoxy system with a low modulus coating on the fibers. The results have been compared with the results obtained from the Sutcu's recursive concentric cylinders model for composites containing coated fibers. From the comparison of results of the unit-cell models (both, two-phase and three-phase) with the results obtained from some other models available in the literature, it is concluded that the overall thermal properties of fiber-reinforced composites evaluated by the unit-cell model can be used as effectively as by any other model.

A Study on the Hydrodynamic Load in a Water Pool When Discharged Air Forms a Bubble Cloud

2006 ◽  
Author(s):  
Ken Uchida ◽  
Seijiro Suzuki
Keyword(s):  
Void Fraction ◽  
Pressure Oscillation ◽  
Numerical Results ◽  
Numerical Dissipation ◽  
Hydrodynamic Load ◽  
Water Pool ◽  
Two Phase ◽  
Bubble Cloud ◽  
Water Region ◽  
Media Layer

This paper presents a numerical and qualitative study on the expected hydrodynamic load-reducing effect of bubbly media near a volumetrically oscillating bubble. In this study, the bubble or bubble cloud is assumed to be spherically symmetric, and its motion is analyzed as a one-dimensional compressible two-phase flow in the radial direction in spherical coordinates. We adopted the CCUP (CIP-Combined Unified Procedure) method, which is a unified analysis method for both compressible and incompressible fluids proposed by Yabe et al. (1991) in order to treat interaction among gas, liquid, and two-phase media, and to avoid large numerical dissipation at density discontinuities. To verify the analysis program we developed, we analyzed free oscillations of a bubble with a unity void fraction and of a bubble cloud with an initial void fraction of 0.5, and found that the natural frequency from numerical results are well reproduced with an error of 0.9% for the bubble and 5% for the bubble cloud as compared to those obtained on a theoretical basis. Using this method, we analyzed the free oscillation of a bubble cloud in which a bubble with a unity void fraction is covered by a bubbly media layer with an initial void fraction of 0.5. Numerical results show that the amplitude of pressure oscillation inside the bubble is about halved, and that a higher mode of oscillation appears when a bubbly media layer covers the bubble. The measured results from a blowdown test we previously reported also shows a similar higher mode of oscillation. The amplitude of pressure oscillation in the water region was apparently reduced when a thick bubbly media layer covers the bubble. Thus, if the bubbly media is ejected from sparger holes prior to the ejection of a high-pressure bubble, the bubbly media might reduce the hydrodynamic load induced in a water pool made by volumetric oscillation of the bubble.

Optimum Configuration of an Expanding-Contracting-Nozzle for Thrust Enhancement by Bubble Injection

2010 ◽  
Author(s):  
Sowmitra Singh ◽  
Jin-Keun Choi ◽  
Georges Chahine
Keyword(s):  
Bubble Dynamics ◽  
Bubbly Flow ◽  
Outlet Section ◽  
Inlet Section ◽  
Concept Design ◽  
Two Phase ◽  
Approximate Analytical Expression ◽  
Analytical Expression ◽  
Bubble Number ◽  
Analytical Approaches

This paper addresses the concept of thrust augmentation through bubble injection into an expanding-contracting nozzle. Two-phase models for bubbly flow in an expanding-contracting nozzle are developed, in parallel with laboratory experiments, and used to ascertain the geometry configuration for the nozzle that would lead to maximum thrust enhancement upon bubble injection. For preliminary optimization of experimental setup’s design, a quasi 1-D approach is used. Averaged flow quantities (such as velocities, pressures, and void fractions) in a cross-section are used for the analysis. The mixture continuity and momentum equations are numerically solved simultaneously, along with equations for bubble dynamics, bubble motion, and an equation for conservation of bubble number. Various geometric parameters such as the exit and inlet areas, the area of the bubble injection section, the presence of a throat and its location, the length of the diffuser section and the length of the contraction section are varied, and their effects on thrust enhancement are studied. Investigation on the effect of the injected void fraction is also carried out. The key objective function of the optimization is the normalized thrust parameter, which is the difference between the thrust with the bubble injection and the thrust before the bubble injection, normalized by the inlet momentum. An approximate analytical expression for the normalized thrust parameter was also derived starting from the mixture continuity and momentum equations. This analytical expression involved flow variables only at three locations; inlet section, injection section, and outlet section, and the expression is simple enough to produce a quick concept design of the diffuser-nozzle thruster. The numerical and analytical approaches are verified against each other and the limitations of the analytical approach are discussed.

Numerical and Experimental Investigation of Bubble Dynamics via Electrowetting-on-Dielectric (EWOD)

2016 ◽  
Author(s):  
Sheng Wang ◽  
Junxiang Shi ◽  
Hsiu-Hung Chen ◽  
Tiancheng Xu ◽  
Chung-Lung (C. L.) Chen
Keyword(s):  
Thin Film ◽  
Contact Angle ◽  
Bubble Dynamics ◽  
Bubble Diameter ◽  
Experimental System ◽  
Hydrophobic Surface ◽  
Numerical Results ◽  
The Body ◽  
Two Phase ◽  
Electrowetting On Dielectric

With the inspiration from electrowetting-controlled droplets, the potential advantages of electrowetting for bubble dynamics are investigated experimentally and numerically. In our experimental system, a 100 nanometer thin film gold metal was used as an electrode, and a 6.5 micrometer polydimethylsiloxane (PDMS) was spin-coated on the electrode acting both as an dielectric layer and hydrophobic surface. A two-phase model coupled with a electrostatics was used in our simulation work, where the body force due to the electric field acts as an external force. Our numerical results demonstrated that electrowetting can help the detachment of a small bubble by changing the apparent contact angle. Similar results were observed in our experiments that with electrowetting on dielectric, the contact angle of bubble on a hydrophobic surface will obviously decrease when a certain electrical field is applied either with a small size bubble (diameter around 1mm) or a relatively larger size bubble (diameter around 3 mm). When the applied voltage becomes high enough, both the experimental and numerical results demonstrate the characteristics of bubble detachment within a thin film liquid layer.

Optimum Configuration of an Expanding-Contracting-Nozzle for Thrust Enhancement by Bubble Injection

2012 ◽  
Vol 134 (1) ◽  
Author(s):  
Sowmitra Singh ◽  
Jin-Keun Choi ◽  
Georges Chahine
Keyword(s):  
Bubble Dynamics ◽  
Bubbly Flow ◽  
Outlet Section ◽  
Inlet Section ◽  
Concept Design ◽  
Two Phase ◽  
Approximate Analytical Expression ◽  
Analytical Expression ◽  
Bubble Number ◽  
Analytical Approaches

This paper addresses the concept of thrust augmentation through bubble injection into an expanding-contracting nozzle. Two-phase models for bubbly flow in an expanding-contracting nozzle are developed, in parallel with laboratory experiments and used to ascertain the geometry configuration for the nozzle that would lead to maximum thrust enhancement upon bubble injection. For preliminary optimization of experimental setup’s design, a quasi 1-D approach is used. Averaged flow quantities (such as velocities, pressures, and void fractions) in a cross section are used for the analysis. The mixture continuity and momentum equations are numerically solved simultaneously along with equations for bubble dynamics, bubble motion, and an equation for conservation of the total bubble number. Various geometric parameters such as the exit and inlet areas, the area of the bubble injection section, the presence of a throat and its location, the length of the diffuser section and the length of the contraction section are varied, and their effects on thrust enhancement are studied. Investigation on the effect of the injected void fraction is also carried out. The key objective function of the optimization is the normalized thrust parameter, which is the thrust with bubble injection minus the thrust with liquid only divided by the inlet liquid momentum. An approximate analytical expression for the normalized thrust parameter was also derived starting from the mixture continuity and momentum equations. This analytical expression involved flow variables only at three locations; inlet section, injection section, and outlet section, and the expression is simple enough to produce a quick concept design of the diffuser-nozzle thruster. The numerical and analytical approaches are verified against each other and the limitations of the analytical approach are discussed.

The f.c.c.+tetragonal two-phase region of the Cu–Ni–Zn system

1983 ◽  
Vol 16 (1) ◽  
pp. 99-102 ◽  
Author(s):  
O. S. Mayall
Keyword(s):  
Tetragonal Phase ◽  
Lattice Spacing ◽  
Single Phase ◽  
Phase Region ◽  
Unit Cell ◽  
Unit Cell Parameters ◽  
Two Phase ◽  
Cell Parameters ◽  
Tie Lines

The f.c.c. + tetragonal two-phase region of the Cu–Ni–Zn system has been delineated, and unit-cell parameters along the boundaries determined. Apparently anomalous parameter measurements prevented the determination of the tie lines. A pattern of diffraction broadening from the tetragonal phase common to both the two-phase and single-phase regions was related to the variation in lattice spacing of the tetragonal phase along the boundary. Reasons for this broadening are discussed.

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